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HW09 12.7-12.8: Problem 18 Previous Problem Problem List Next Problem (1 point) Suppose a change of coordinates T : R2 + R2 from the uv-plane to the by-plane is given by I= -30 – 3u - 1. y = -1 +54 + 2v. (a) Find the absolute value of the determinant of the Jacobian for this change of coordinates a(z,y) a(u, v) det - 1 (b) If a region D* in the uv-plane has area 7.14, find the area of the region T(D) in the zy-plane. Area = Note: You can earn partial credit on this problem Preview My Answers Submit Answers You have attempted this problem 0 times. You have unlimited attempts remaining.

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ANSWER:

Given T: R² R² 2= -3V-34-1, y+54 + 2V ) ca) X = -38-34-) y = -1+54 +2V @ from 0, ax an -3 die av 2-3 from dy dy 5) 11 2 W ди dv dx au ax dv aca.yg det ay acuiv) ду du av det -3 5 2 - 6+15 9

9 drary) acuiu) b) Given Uv-plane Area = 7.14 as if area in Un.. plane is k, then area in xy.plane for the same region is always deary) k dcu, v) 9x7.14 = 64.26 ... The required Area 64.26